Conductance plateau transitions in quantum Hall wires with spatially correlated random magnetic fields

Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated with the edge state, in contrast to the naive expectation that the correlation simply reduces the effect of disorder. In the presence of correlation, the separation between the successive conductance plateau transitions becomes larger than the bulk Landau level separation determined by the mean value of the disordered magnetic fields. The transition energies coincide with the Landau levels in an effective magnetic field stronger than the mean value of the disordered magnetic field. For a long wire, the strength of this effective magnetic field is of the order of the maximum value of the magnetic fields in the system. It is shown that the effective field is determined by a part where the stronger magnetic field region connects both edges of the wire.Comment: 7 pages, 10 figure

Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign

Quantum transport in disordered magnetic fields is investigated numerically in two-dimensional systems. In particular, the case where the mean and the fluctuation of disordered magnetic fields are of the same order is considered. It is found that in the limit of weak disorder the conductivity exhibits a qualitatively different behavior from that in the conventional random magnetic fields with zero mean. The conductivity is estimated by the equation of motion method and by the two-terminal Landauer formula. It is demonstrated that the conductance stays on the order of $e^2/h$ even in the weak disorder limit. The present behavior can be interpreted in terms of the Drude formula. The Shubnikov-de Haas oscillation is also observed in the weak disorder regime.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Topologically protected Landau levels in bilayer graphene in finite electric fields

The zero-energy Landau level of bilayer graphene is shown to be anomalously sharp (delta-function like) against bond disorder as long as the disorder is correlated over a few lattice constants.The robustness of the zero-mode anomaly can be attributed to the preserved chiral symmetry. Unexpectedly, even when we apply a finite potential difference (i.e., an electric field) between the top and the bottom layers, the valley-split $n=0$ Landau levels remain anomalously sharp although they are now shifted away from the zero energy, while the $n=1$ Landau levels exhibit the usual behavior.Comment: 5 pages, 5 figure

Magnetotransport in inhomogeneous magnetic fields

Quantum transport in inhomogeneous magnetic fields is investigated numerically in two-dimensional systems using the equation of motion method. In particular, the diffusion of electrons in random magnetic fields in the presence of additional weak uniform magnetic fields is examined. It is found that the conductivity is strongly suppressed by the additional uniform magnetic field and saturates when the uniform magnetic field becomes on the order of the fluctuation of the random magnetic field. The value of the conductivity at this saturation is found to be insensitive to the magnitude of the fluctuation of the random field. The effect of random potential on the magnetoconductance is also discussed.Comment: 5 pages, 5 figure

Spin and orbital effects in a 2D electron gas in a random magnetic field

Using the method of superbosonization we consider a model of a random magnetic field (RMF) acting on both orbital motion and spin of electrons in two dimensions. The method is based on exact integration over one particle degrees of freedom and reduction of the problem to a functional integral over supermatrices $Q({\bf r},{\bf r^{\prime}})$. We consider a general case when both the direction of the RMF and the g-factor of the Zeeman splitting are arbitrary. Integrating out fast variations of $Q$ we come to a standard collisional unitary non-linear $\sigma$-model. The collision term consists of orbital, spin and effective spin-orbital parts. For a particular problem of a fixed direction of RMF, we show that additional soft excitations identified with spin modes should appear. Considering $\delta$% -correlated weak RMF and putting g=2 we find the transport time $\tau_{tr}$. This time is 2 times smaller than that for spinless particles.Comment: 9 pages, no figure

Novel Studies on the \eta' Effective Lagrangian

The effective Lagrangian for \eta' incorporating the effect of the QCD \theta-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the \eta'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.Comment: 14 pages, 1 figure; V2: NEW TITLE; revised version to be published in JHEP; references adde

Anomalous diffusion at the Anderson transitions

Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $$ at the Anderson transition is shown to behave as $\sim t^a (a\approx 2/3)$. From the temporal autocorrelation function $C(t)$, the fractal dimension $D_2$ is deduced, which is almost half the value of space dimension for all the universality classes.Comment: Revtex, 2 figures, to appear in J. Phys. Soc. Jpn.(1997) Fe

Energy-level statistics and localization of 2d electrons in random magnetic fields

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.Comment: 4 pages LaTeX, 4 eps-figures. to appear in Physica

Anderson transition of three dimensional phonon modes

Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is shown to be in excellent agreement with the energy level statistics of the disrodered electron system belonging to the orthogonal universality class.Comment: 2 pages and another page for 3 figures, J. Phys. Soc. Japa